216 research outputs found
Angular diameter distances reconsidered in the Newman and Penrose formalism
Using the Newman and Penrose spin coefficient (NP) formalism, we provide a
derivation of the Dyer-Roeder equation for the angular diameter distance in
cosmological space-times. We show that the geodesic deviation equation written
in NP formalism is precisely the Dyer-Roeder equation for a general
Friedman-Robertson-Walker (FRW) space-time, and then we examine the angular
diameter distance to redshift relation in the case that a flat FRW metric is
perturbed by a gravitational potential. We examine the perturbation in the case
that the gravitational potential exhibits the properties of a thin
gravitational lens, demonstrating how the weak lensing shear and convergence
act as source terms for the perturbed Dyer-Roeder equation.Comment: 21 pages, 6 figures, accepted to GR
Five is 75: Student Success Perspectives, Status, & Highlights
Bridgewater State University\u27s incoming first-time, full-time freshmen cohorts have included about 1,500 students since 2007. A 5% gain in the overall graduation rate means helping 75 additional students achieve their goals. Many schools have achievement gaps between male and female students, but Bridgewater State University has typically had larger gaps than other institutions in its peer group. In recent years, Bridgewater has been particularly concerned about the graduation and retention rates for men of color. In data presented in this poster, we show that there is strong evidence that the overall performance of men of color has improved significantly, but that gender differences persist in general. Unlike students of color, there have been only very minimal closings in the achievement gaps for low income and first generation students
Spacetime perspective of Schwarzschild lensing
We propose a definition of an exact lens equation without reference to a
background spacetime, and construct the exact lens equation explicitly in the
case of Schwarzschild spacetime. For the Schwarzschild case, we give exact
expressions for the angular-diameter distance to the sources as well as for the
magnification factor and time of arrival of the images. We compare the exact
lens equation with the standard lens equation, derived under the
thin-lens-weak-field assumption (where the light rays are geodesics of the
background with sharp bending in the lens plane, and the gravitational field is
weak), and verify the fact that the standard weak-field thin-lens equation is
inadequate at small impact parameter. We show that the second-order correction
to the weak-field thin-lens equation is inaccurate as well. Finally, we compare
the exact lens equation with the recently proposed strong-field thin-lens
equation, obtained under the assumption of straight paths but without the small
angle approximation, i.e., with allowed large bending angles. We show that the
strong-field thin-lens equation is remarkably accurate, even for lightrays that
take several turns around the lens before reaching the observer.Comment: 22 pages, 6 figures, to appear in Phys. Rev.
Study of errors in strong gravitational lensing
We examine the accuracy of strong gravitational lensing determinations of the
mass of galaxy clusters by comparing the conventional approach with the
numerical integration of the fully relativistic null geodesic equations in the
case of weak gravitational perturbations on Robertson-Walker metrics. In
particular, we study spherically-symmetric, three-dimensional singular
isothermal sphere models and the three-dimensional matter distribution of
Navarro et al. (1997), which are both commonly used in gravitational lensing
studies. In both cases we study two different methods for mass-density
truncation along the line of sight: hard truncation and conventional (no
truncation). We find that the relative error introduced in the total mass by
the thin lens approximation alone is less than 0.3% in the singular isothermal
sphere model, and less than 2% in the model of Navarro et al. (1997). The
removal of hard truncation introduces an additional error of the same order of
magnitude in the best case, and up to an order of magnitude larger in the worst
case studied. Our results ensure that the future generation of precision
cosmology experiments based on lensing studies will not require the removal of
the thin-lens assumption, but they may require a careful handling of
truncation.Comment: accepted to Ap
Continuous image distortion by astrophysical thick lenses
Image distortion due to weak gravitational lensing is examined using a
non-perturbative method of integrating the geodesic deviation and optical
scalar equations along the null geodesics connecting the observer to a distant
source. The method we develop continuously changes the shape of the pencil of
rays from the source to the observer with no reference to lens planes in
astrophysically relevant scenarios. We compare the projected area and the ratio
of semi-major to semi-minor axes of the observed elliptical image shape for
circular sources from the continuous, thick-lens method with the commonly
assumed thin-lens approximation. We find that for truncated singular isothermal
sphere and NFW models of realistic galaxy clusters, the commonly used thin-lens
approximation is accurate to better than 1 part in 10^4 in predicting the image
area and axes ratios. For asymmetric thick lenses consisting of two massive
clusters separated along the line of sight in redshift up to \Delta z = 0.2, we
find that modeling the image distortion as two clusters in a single lens plane
does not produce relative errors in image area or axes ratio more than 0.5%Comment: accepted to GR
Wide-field weak lensing by RXJ1347-1145
We present an analysis of weak lensing observations for RXJ1347-1145 over a
43' X 43' field taken in B and R filters on the Blanco 4m telescope at CTIO.
RXJ1347-1145 is a massive cluster at redshift z=0.45. Using a population of
galaxies with 20<R<26, we detect a weak lensing signal at the p<0.0005 level,
finding best-fit parameters of \sigma_v=1400^{+130}_{-140} km s^{-1} for a
singular isothermal sphere model and r_{200} = 3.5^{+0.8}_{-0.2} Mpc with c =
15^{+64}_{-10} for a NFW model in an \Omega_m = 0.3, \Omega_\Lambda = 0.7
cosmology. In addition, a mass to light ratio M/L_R =90 \pm 20 M_\odot /
L_{R\odot} was determined. These values are consistent with the previous weak
lensing study of RXJ1347--1145 by Fischer and Tyson, 1997, giving strong
evidence that systemic bias was not introduced by the relatively small field of
view in that study. Our best-fit parameter values are also consistent with
recent X-ray studies by Allen et al, 2002 and Ettori et al, 2001, but are not
consistent with recent optical velocity dispersion measurements by Cohen and
Kneib, 2002.Comment: accepted to ApJ, tentative publication 10 May 2005, v624
Fermat Potentials for Non-Perturbative Gravitational Lensing
The images of many distant galaxies are displaced, distorted and often
multiplied by the presence of foreground massive galaxies near the line of
sight; the foreground galaxies act as gravitational lenses. Commonly, the lens
equation, which relates the placement and distortion of the images to the real
source position in the thin-lens scenario, is obtained by extremizing the time
of arrival among all the null paths from the source to the observer (Fermat's
principle). We show that the construction of envelopes of certain families of
null surfaces consitutes an alternative variational principle or version of
Fermat's principle that leads naturally to a lens equation in a generic
spacetime with any given metric. We illustrate the construction by deriving the
lens equation for static asymptotically flat thin lens spacetimes. As an
application of the approach, we find the bending angle for moving thin lenses
in terms of the bending angle for the same deflector at rest. Finally we apply
this construction to cosmological spacetimes (FRW) by using the fact they are
all conformally related to Minkowski space.Comment: accepted for publication in Phys. Rev.
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